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ir7
  • Member for 10 years, 5 months
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11 votes
Accepted

How prove this inequality $\left(\int_{0}^{1}f(x)dx\right)^2\le\frac{1}{12}\int_{0}^{1}|f'(x)|^2dx$

9 votes
Accepted

Is the pull back of a generated $\sigma$-algebra itself a generated $\sigma$-algebra?

8 votes
Accepted

How do I transform an r.v. using the floor function? (exponential distribution)

7 votes

How to explain to a high school student why a linear differential equation is linear?

6 votes

Cauchy convergence in probability implies the existence of a (finite a.e.) limit $X$

6 votes

General formula of repeated roots.

6 votes

Continuity of conjugate of $z$: $f(z)=\bar z$

6 votes
Accepted

Convergence in distribution ( Two equivalent definitions)

6 votes

showing the equation is true

6 votes
Accepted

The existence of group isomorphism between Euclidean space.

6 votes

Show $\log(\det(A))\le \operatorname{tr}(A)-n$

5 votes

How find this $\left(\frac{1}{x^2+a^2}\right)^{(n)}$

5 votes

What is the gradient of $f(x, y, z) = \sqrt{x^2+y^2+z^2}$?

5 votes

Interesting locus

5 votes

What is the intuition behind Chebyshev's Inequality in Measure Theory

4 votes

Find all $z\in\Bbb C$ such that $|z+1|+ |z-1|=4$

4 votes
Accepted

How to find the volume of a irregular tetrahedron, when I know the length of all sides?

4 votes
Accepted

Show that F(X) and Y-E[Y|X] uncorrelated

4 votes
Accepted

Proof of Markov's inequality using alternate form of expectation

4 votes
Accepted

Discontinuity of the characteristic function

4 votes

If $x+\frac1x=5$ find $x^5+\frac1{x^5}$.

4 votes
Accepted

Is there a closed-form for $\sum_{n=0}^{\infty}\frac{n}{n^3+1}$?

4 votes

Polya's urn (martingale)

4 votes
Accepted

A maximal element of the set of non-principal ideals is prime

4 votes

How to prove this equality of the determinant of matrix?

3 votes

Proving a limit using the $\epsilon$ - $\delta$ definition of limit.

3 votes

Finite differences second derivative as successive application of the first derivative

3 votes

Prove that $|a + b| = |a| + |b| \iff a\overline{b} \ge 0$

3 votes
Accepted

Preservation of convergence in measure by absolutely continuous measures

3 votes

Quotient of ring by radical ideal.

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